Why do CDG flights to LAX (or vice-cersa) often fly over Greenland, ie a "Polar" route.
I know this is to save time (shorter route), but when the route is sometimes more to the South, the flight is finally not longer.
Your thoughts?

It is all about wind. Over the north atlantic you have strong jetstreams. On the westbound part you fly against the wind, so you fly a detour to avoid the headwinds, but the flight is still shorter (flight time wise). The distance maybe longer, but the shorter the flight time, the less fuel you use.
On the eastbound flight you want to use the strong winds as tailwinds, so you fly a route where you have strong tailwinds. Make the flight shorter (flight time wise)... So a detour in aviation can mean reducing flight time - because of the winds.

According to FAA, a route is polar if it is north of 78 degrees north. Since that is further north of almost anywhere in N. America or even Greenland, I doubt AF ventures into this territory. In fact, are there any polar routes from Europe to N. America? Did the SVO-SEA flight go that north?